Communication system performance is enhanced by both power and bandwidth efficiencies. Since 1993, turbo codes have been shown to be powerful forward error correction codes that enhance communication system performance. Many commercial communication systems use turbo codes as standards through the development of standard turbo codeces. Although a significant amount of coding gain can be achieved, the binary turbo codes do not have good bandwidth efficiency due to low code rates unless heavily punctured with additional coding bits. Heavily punctured turbo coding results in bit-error-rate (BER) performance degradation. Conventional approaches to improving bandwidth efficiencies are to adopt turbo trellis coded modulation (TTCM). For most TTCM structures, each modulated symbol corresponds to a state transition during modulation where a respective metric is computed for each received symbol during reception. A TTCM system can provide good turbo code performance without bandwidth expansion. However, a TTCM system requires a different code structure than a conventional binary turbo code. Each unique turbo code design results in an expensive new codec development.
One way to attain both power and bandwidth efficiencies is to adopt high-order modulation schemes with a binary turbo code. An alternative to a TTCM structure for obtaining both power and bandwidth efficiency is to adopt high-order nonbinary modulation such as M-ary phase shift keying (PSK) modulation or M-ary quadrature amplitude modulation (QAM). High-order nonbinary modulation structures include, for examples, the commonly used 8-ary PSK or 16-ary PSK, with a commonly used binary turbo code, or for examples, the commonly used 16-ary QAM, or 64-ary QAM, with a commonly used binary turbo code. These high-order nonbinary modulation methods require a conversion of demodulator output that is associated with the nonbinary channel symbol into bit metrics as inputs to the binary turbo decoder. The advantage of M-ary nonbinary modulation is that no new codec development is required because the binary turbo codeces are commercially available. However, the problem with M-ary nonbinary modulation is the need to implement improved methods of forming the bitwise decoding metrics on binary bits from the nonbinary demodulator. For most TTCM structures, each modulated symbol has a state with a transition from one state to another state defining a metric distance. The maximum likelihood metric, which is associated with the minimum Euclidean distance, is formed at the demodulator and used for turbo decoding. However, for the binary turbo coding, the bitwise metrics must be formed for turbo decoding.
One way to form the bitwise decoding metrics from a PSK or a QAM demodulator is to use the maximum likelihood metric that is the optimum one for uncoded demodulation as widely used. Unfortunately, forming this metric requires complex circuitry and knowledge of channel condition, which is sometimes unavailable. More importantly, this decoding metric gives inferior bit-error-rate (BER) performance to the TTCM system. A puncturing approach is applied to a trellis coded modulation using a turbo coding, such as a rate (m−1)/m binary convolutional code punctured from an optimum and widely used rate 1/2 convolutional code followed by a 2L-ary PSK or QAM modulation, where L is the number of bits in a symbol. A property of this puncturing approach is that a complicated mapping is used for the signal constellation. Common puncturing converts a commonly used turbo code into a rate turbo code of rate m′/m, where m′<m, for an 2L-ary high order binary modulation. A gray code approach can be used where gray code mapping defines a signal constellation space and can be used during turbo coding that also utilizes puncturing for improved bandwidth efficiency. However, when m′/m is greater than 1/2, more than 50% of parity check bits need to be discarded, which can cause additional BER degradation. These and other disadvantages are solved or reduced using the invention.